function Spiral_of_black_and_white_squares()
% source code for drawing the animation
%
% 2017-04-26 Jahobr

fps = 50;
[pathstr,fname] = fileparts(which(mfilename)); % save files under the same name and at file ___location

figHandle = figure(15124455);
clf
axesHandle = axes;
hold(axesHandle,'on')
set(figHandle, 'Units','pixel');
set(figHandle, 'position',[1 1 1000 1000]); % set default
set(axesHandle,'position',[0 0 1 1]); % stetch axis bigger as figure, easy way to get rid of ticks [x y width hight]
set(figHandle,'GraphicsSmoothing','on') % requires at least version 2014b

L(1) = 1; % definition, length of first square

xyLim = [-L(1) L(1)]*0.99;
xlim(xyLim); ylim(xyLim); % set axis limits
axis equal; drawnow;

for nSquaresTillRep = [4 10] % ONLY EVEN NUMBERS! number of squares till the orientation repeats (90°)
    
    alpha = pi/2/nSquaresTillRep;
    
    %    +--a1--+==----b1------+
    %    I     /   ----____    a1
    %    b1   /            ----+
    %    I   /            90° /I<-alpha
    %    I  /                / I
    %    I /                /  I
    %    I/                /   b1
    %    +---___          /    I
    %    a1     ----___  /     I
    %    +----b1-------=+--a1--+
    
    for index = 1:nSquaresTillRep+1
        % L = a+b
        % tan(alpha) = a/b; tan(alpha)*b = a
        % 1 = tan(alpha)*b+b = b*(tan(alpha)+1)
        b(index) = L(index)/(tan(alpha)+1);
        a(index) = L(index)-b(index);
        
        L(index+1) = sqrt(a(index)^2+b(index)^2); % side length of inner square
    end
    
    for currentCase = 1:2
        switch currentCase
            case 1 % zoom
                nFrames = 200;
                set(figHandle, 'position',[1 1 500 500]); % 
                method = 'zooming_in';
                endVal = log( 1/L(nSquaresTillRep+1) );
                scale = linspace(0,endVal,nFrames+1);
                
                scale = exp(scale);
                scale = scale(1:end-1); % cut of doubled frame
                rotImage = linspace(0,-pi/2,nFrames+1);
                rotImage = rotImage(1:end-1); % cut of doubled frame
            case 2 % spiral
                if nSquaresTillRep == 4
                    nFrames = 100;
                    set(figHandle, 'position',[1 1 700 700]); % 
                elseif  nSquaresTillRep == 10
                    nFrames = 50;
                    set(figHandle, 'position',[1 1 1000 1000]); % 
                else
                    error('not defined')
                end
                method = 'spiraling_in';
                endVal = log( 1/L(3) );
                scale = linspace(0,endVal,nFrames+1);
                
                scale = exp(scale);
                scale = scale(1:end-1); % cut of doubled frame
                rotImage = linspace(0,-2*alpha,nFrames+1);
                rotImage = rotImage(1:end-1); % cut of doubled frame
        end
        
        sb = b(1); % scale square down one itteration (assuming  a(1)+b(1)=1)
        sa = a(1); % scale square down one itteration (assuming  a(1)+b(1)=1)
        
        for iFrame = 1:nFrames
            cla(axesHandle) % fresh frame
            
            col = [0 0 0]; % start black
            
            curScale = scale(iFrame);
            x = curScale*[-L(1) -L(1) L(1)  L(1)]; % make base square bigger, to "zoom in"
            y = curScale*[-L(1)  L(1) L(1) -L(1)]; % make base square bigger, to "zoom in"
            
            if currentCase == 2 % rotate base square
                rotM = [cos(-rotImage(iFrame)) -sin(-rotImage(iFrame)); sin(-rotImage(iFrame)) cos(-rotImage(iFrame))];
                vecTemp = rotM*[x; y];
                x = vecTemp(1,:);
                y = vecTemp(2,:);
            end
            
            while norm([x(1) y(1)]) > 0.5/900 % squares smaller than a pixel
                
                patch([x x(1)],[y y(1)],col,'EdgeColor','none');
                
                col = 1-col; % flip color
                
                x = [sb*x(1)+sa*x(2)  sb*x(2)+sa*x(3)  sb*x(3)+sa*x(4)  sb*x(4)+sa*x(1)]; % create next square
                y = [sb*y(1)+sa*y(2)  sb*y(2)+sa*y(3)  sb*y(3)+sa*y(4)  sb*y(4)+sa*y(1)]; % create next square
                
            end
            
            %% save animation
            xlim(xyLim); ylim(xyLim); % set axis limits
            drawnow % update figure window and execute pending callbacks
            pause(0.01)
            
            f = getframe(figHandle);

            if iFrame== 1
                map = gray(8); % 8 colors % create color map % or use : [im,map] = rgb2ind(f.cdata,4,'nodither'); % 
                im = rgb2ind(f.cdata,map,'nodither'); % create first image
                
                im(1,1,1,nFrames) = 0; % allocate
                if currentCase == 1
                    if ~isempty(which('plot2svg'))
                        plot2svg(fullfile(pathstr, [fname '_' num2str(nSquaresTillRep)  '_till_repetition.svg']),figHandle) % by Juerg Schwizer, See http://www.zhinst.com/blogs/schwizer/
                    else
                        disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/');
                    end
                end
            end
            
            imtemp = rgb2ind(f.cdata,map,'nodither');
            im(:,:,1,iFrame) = imtemp;
            
        end
        imwrite(im,map,fullfile(pathstr, [fname '_'  num2str(nSquaresTillRep) '_till_repetition_' method '.gif']),'DelayTime',1/fps,'LoopCount',inf) % save gif
        disp([fname '_'  num2str(nSquaresTillRep) '_till_repetition_' method '.gif  has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 50 MP limit
    end
end